2 Answers
2

used to emphasize something surprising or extreme : they have never even heard of the U.S. | they wore fur hats, even in summer. [NOAD]

It is merely a kind of intensifier, usually used to express the outrageousness of a thing. Now let's get down to cases:

Are you even listening?

The speaker doubts you are listening and is rebuking you for your inattention.

What time does the shop even close?

This one's a little harder, but probably someone has suggested the speaker go to this shop and the speaker doubts that it's open, or else someone has suggested that shop may be closed but the speaker is emphasizing the fact that the shop in fact stays open quite late. It would depend on context.